Game Theory - A Model Explaining Driver’s Behavior in the Hong Kong Context

 

There are 3 key factors to consider when explaining how a single driver makes his choice:

• Time Component - Travel time without any barrier

• Price Component – Toll Fee

• Flow Component - Additional travel time due to existence of other road users

 

In the model, time component and price component is first considered. These two components are incorporated so that a Price+Time component in terms of unit – Price. The mechanism will be explained underneath.

 

There are three assumptions. First, it is assumed that all drivers drive in a speed of 50km/h so that for the same distance, all drivers have same travel time. Second, it is assumed that all drivers have income of $14100 per month (which is the median disposal income) so that they have the same “price” for one minute. Third, only private car is considered so that each car is charged the same toll fee.

 

Under these assumptions, the two components could be incorporated together and a Price+Time component could be deduced by transferring travel time in to money terms.

 

The time component and price component will be different if a driver chooses different tunnels to cross the harbor. A reasonable man will choose the tunnel that has the lowest Price+Time Component

 

Here is an example to help you understand the concept:

 

If you are a driver want to reach Red Point from Green Point, which tunnel will you choose if the effect of other cars is omitted?

 

 

 

 

 

 

 

 

 

 

 

Here we made a table to help you consider:

 

 

 

 

 

 

 

 

 

 

 

 

According to the table, the Price-Time component of CHT is the lowest. Therefore, a driver will choose CHT which is reasonable as it is the cheapest and facilitates the shortest travel distance.

 

When the Price+Time component of a tunnel is higher, the probability for a driver to choose that tunnel is lower. Under this rational, given a certain number of cars, the distribution of traffic flow will be 0.1951, 0.4667 and 0.3382 respectively (WHC, CHT and EHT).

 

But when existence of other road users is considered, the calculation is not as simple as above. Flow component is therefore incorporated. The rational is, when you see there are lots of car using CHT, you may rather drive to EHC or WHC and payer higher toll fee in exchange of the chance of less journey time.

 

According to the result of 0.1951, 0.4667 and 0.3382, one may prefer to go WHC to avoid congestion. After such psychological factor is considered, the final result will be 0.2257, 0.441 and 0.3333. Nash equilibrium under this set of toll fee is hereby achieved. Theoretically, no one can lower his Price+Time component by choosing another tunnel.

 

This result shows that cars going through EHT are more or less the same but there are more cars going through WHC.

 

Of course, for different drivers, they might have different starting point and ending point. Considering only one route is not convincing. To facilitate this, 3 entrance point and 3 exit point was identified under which a driver could access to anywhere in Hong Kong through the Highway System.

 

 

 

 

 

 

 

 

 

 

 

 

Also, only northbound traffic is considered for easy calculation. This will not affect the result as northbound traffic and southbound traffic are using two different roads which will not affect each other.

 

After the process of trial-and-error, an optimal price set that result in an equalized traffic distribution is achieved.

 

The calculation could be downloaded by clicking HERE.